I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1. But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1. But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

The Fool: You are conflating symbolization limits, with conceptual.

"The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

I presume you mean 1/9 not 1/0, and the reason I know it is because I can understand and do simple division.

You can do simple division? I can prove a finite series of decimals is equal to a fraction easily because of the definition of a fraction (.1 equals 1/10) so 1/5 is .2 because 5 goes into ten twice. But how many times does 9 go into 10? It goes on forever. I'm not sure it's possible to prove 1/9 is equal to .111.

As far as mathematics is concerned, proofs are pretty convincing, it's a simple fact that 1 = .999

At 3/28/2013 2:34:38 PM, natoast wrote:I had a thought during calculus today. Normally I would consider .999 repeating to be as close you can possibly get to 1 with being 1.

999... is equal to one.

But then I considered the fact that .9 was just 1/10 less than one, because we use a base 10 counting system. But in a base 11 counting system, the largest single digit decimal would be 0.(10), which would be larger than .9. So it seems to me that 0.(10)(10)(10) repeating would be closer to 1 than .999 repeating. I suppose this means that .999 repeating is not equal to 1-1/infinity. Does this stand up to reason, or is it an established mathematical fact I was not aware of?

At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.43/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater

At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.43/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

In base twelve a third is written as 0.4. Base twelve makes mathematics easier. Yes, it is still the same amount, it's just easier to use in equations.

At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.43/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

In base twelve a third is written as 0.4. Base twelve makes mathematics easier. Yes, it is still the same amount, it's just easier to use in equations.

Yes, but in base twelve 1/5 and 1/7 are repeating decimals, a base twelve counting system does not does not give a finite representation for all fractions so it just doesn't solve the problem of repeating decimals. There might be fewer repeating decimals, but you still have them.

Plus, I really don't think it's all that practical to change the worldwide counting system, especially since you might just be the only person in the world that thinks a duodecimal system is "just easier".

"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater

At 4/4/2013 9:21:06 AM, AlbinoBunny wrote:It is a failing with our base system. You can use such things to consider mathematics and infinity though.

In a different thread I suggested that base twelve is better than base ten.

In base ten: 1/3 = 0.333333...3/3 = 0.999999... or 1.

In base twelve: 1/3 = 0.43/3 = 1.

Base twelve doesn't solve anything, one third is one third, it still gives a repeating decimal, 4/12 is .333... so in base twelve it would be 4/10 that would equal .333...it doesn't change anything.

Repeating decimals are simple grade school stuff, the fact that they are repeating doesn't make it some mysterious infinity thing, they just repeat when certain fractions are translated into a decimal system of notation..

In base twelve a third is written as 0.4. Base twelve makes mathematics easier. Yes, it is still the same amount, it's just easier to use in equations.

Yes, but in base twelve 1/5 and 1/7 are repeating decimals, a base twelve counting system does not does not give a finite representation for all fractions so it just doesn't solve the problem of repeating decimals. There might be fewer repeating decimals, but you still have them.

Plus, I really don't think it's all that practical to change the worldwide counting system, especially since you might just be the only person in the world that thinks a duodecimal system is "just easier".

There are less repeating "decimals" and more shorter "decimals" as well. And the multiplications are easier. It also works better with any multiple of two, three or either. I'm not the only person, once you get used to it it's easier. If you taught it in parallel with decimal to kids they'd probably wonder why we use decimal. The gains aren't huge, but when compounded it's enough to consider whether it should be used in parallel with decimal.